German Published Patent Application DE-A1-4,030,881 discloses a slip control system for the driven wheels of a motor vehicle wherein the rotational velocities of the driven wheels w.sub.L and w.sub.R and the engine rpm w.sub.eng are determined and wherein a controller determines desired braking moments M.sub.BL * and M.sub.BR * for the driven wheels from the difference between the rotational velocities of the wheels .DELTA.w=(w.sub.L -w.sub.R) and the engine rpm w.sub.eng, with the desired braking moments being converted to valve actuation times for the brakes of these wheels. There, too, the same input values are employed and there, too, the difference .DELTA.w between the rotational velocities of the driven wheels serve as a control criterion. Finally, the system disclosed there also includes an attenuation controller which coprocesses the rate of rotation of the engine.